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RSB [31]
3 years ago
8

Fernell and Dabney shared the driving

Mathematics
1 answer:
Agata [3.3K]3 years ago
5 0

Answer:

15 hours

Step-by-step explanation:

Given:

Fernell's speed v_F= 50 mph

Dabney's speed v_D= 64 mph

Denote:

D_F - distance covered by Fernell

D_D - distance covered by Dabney

t_F - Fernell's time

t_D - Dabney's time

1. If Fernell drove for 3 hours longer than Dabney, then his time is 3 hours more than Dabney's time and

t_F=t_D+3

2. If Fernell covered 18 miles less than Dabney, then

D_D-D_F=18

Use formula D=t\cdot v

D_D=v_D\cdot t_D\Rightarrow D_D=64\cdot t_D\\ \\D_F=v_F\cdot t_F\Rightarrow D_F=50\cdot (t_D+3)

Subtract from the first equation the second equation and equate it to 18:

64t_D-50(t_D+3)=18\\ \\64t_D-50t_D-150=18\\ \\14t_D=168\\ \\t_D=12\ \text{hours}

t_F=t_D+3=12+3=15\ \text{hours}

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